Chapter 3 Linear Systems and Matrices - 3.8 Use Inverse Matrices to Solve Linear Systems - 3.8 Exercises - Skill Practice - Page 214: 15

$$X=\begin{pmatrix}-3&1\\ \frac{11}{2}&-\frac{1}{4}\end{pmatrix}$$

Isolating X by taking the inverse of the matrix, we find: $$\begin{pmatrix}-1&0\\ 6&4\end{pmatrix}X=\begin{pmatrix}3&-1\\ 4&5\end{pmatrix} \\ X=\begin{pmatrix}-1&0\\ 6&4\end{pmatrix}^{-1}\begin{pmatrix}3&-1\\ 4&5\end{pmatrix} \\ X=\begin{pmatrix}-3&1\\ \frac{11}{2}&-\frac{1}{4}\end{pmatrix}$$